Consider that in slope-intercept form the equation of a line is given by:
y = mx + b
where m is the slope and b the y-intercept.
Then, solve for y the given equation, as follow:
2x - 3y = -6 subtract 2x both sides
-3y = -2x - 6 divide by -3 both sides
y = 2/3 x + 2
The previous result is the equation is slope-intercept form.
The graph the previous equation, use the a pair of values for x and placed them in the coordinate system, after this, draw a straigh line which crosses the two points, as follow:
where we have use the values of x = -3 and x = 0 and the results for y are:
y = 2/3 (-3) + 2 = - 2 + 2 = 0
y = 2/3(0) + 2 = 2
Which correspond to the shown points (-3,0) and (0,2)
